10. Let X be the set of real numbers, and let d be the pseudometric given by d(x, y) = 1 if zy, and d(z, z) = 0 (Example 1.1(e)). (a) Describe the closure of the cell C(0; 1). (b) Describe the set B(0:1) = {y E X: d(0, y) ≤ 1}.
10. Let X be the set of real numbers, and let d be the pseudometric given by d(x, y) = 1 if zy, and d(z, z) = 0 (Example 1.1(e)). (a) Describe the closure of the cell C(0; 1). (b) Describe the set B(0:1) = {y E X: d(0, y) ≤ 1}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Basic Pseudometric space: For the question 10b, the solution was provided in 2nd photo, can you look over it and produce the graph of the set described?
![1
us.bbcollab.com/collab/ui/session/playback
bQb
5:17
(ETS
Good Morning!
new HW 2.1 #4,5
106) X = R
Bb
土 日 日 0
f!
R
C) (A₂)
d (x,y) = { 0 if x=y
= discrete pm
B (0 ; 1) = {y EX : d(0₁y) ≤ 1} = R
Ent
( [('=)) 12 =
= [1/2,1]
|0|0
2) X
d
A
A
1
O
17](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9787c00-cfcc-43da-9235-b2564f9dd12e%2Fa92f2f3a-c907-48c1-9ba8-9ea7580b2dc7%2F9m1xb52_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
us.bbcollab.com/collab/ui/session/playback
bQb
5:17
(ETS
Good Morning!
new HW 2.1 #4,5
106) X = R
Bb
土 日 日 0
f!
R
C) (A₂)
d (x,y) = { 0 if x=y
= discrete pm
B (0 ; 1) = {y EX : d(0₁y) ≤ 1} = R
Ent
( [('=)) 12 =
= [1/2,1]
|0|0
2) X
d
A
A
1
O
17
![30 Chapter 1 Pseudometric Spaces
Exercises
10. Let X be the set of real numbers, and let d be the pseudometric given by
d(x, y) = 1 if z #y, and d(x,x) = 0 (Example 1.1(e)).
(a) Describe the closure of the cell C(0; 1).
(b) Describe the set B(0:1) = {y E X: d(0, y) ≤ 1}.
11. Let (X. d) be a pseudometric space, and suppose d has the property that
d(a, b) > 0 whenever a b. Prove that every finite subset of X is closed.
12. Let (X, d) be the space of real numbers with the usual pseudometric. For each
positive integer n, let A₁ = (1/n, 1]. Find cl(U{A}), and find U{cl(An)}.
An](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9787c00-cfcc-43da-9235-b2564f9dd12e%2Fa92f2f3a-c907-48c1-9ba8-9ea7580b2dc7%2Fuldneb9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:30 Chapter 1 Pseudometric Spaces
Exercises
10. Let X be the set of real numbers, and let d be the pseudometric given by
d(x, y) = 1 if z #y, and d(x,x) = 0 (Example 1.1(e)).
(a) Describe the closure of the cell C(0; 1).
(b) Describe the set B(0:1) = {y E X: d(0, y) ≤ 1}.
11. Let (X. d) be a pseudometric space, and suppose d has the property that
d(a, b) > 0 whenever a b. Prove that every finite subset of X is closed.
12. Let (X, d) be the space of real numbers with the usual pseudometric. For each
positive integer n, let A₁ = (1/n, 1]. Find cl(U{A}), and find U{cl(An)}.
An
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